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Herd immunity is something can be relatively easily shown with mathematics.

A huge amount of research into how vaccines are deployed is, and is done by, people with skill in applied mathematics.

Herd immunity is a "tragedy of the commons" type of game. Case closed. Unless you can prove that a rational actor would chose in his own self-interest to cooperate in which case you might get considered for a Nobel prize in economics.

Whether or not we can achieve herd immunity is a tragedy of the commons type game, though it's hardly "case closed" - I know several researchers working in that particular area. The existence of herd immunity is a relatively easy calculus problem.

Your argument could also be applied to paying taxes, which is why that's legally mandated.

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